MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2024: question 38

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section E, question 38, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q38 · 4 marks · Case-basedCompetency-basedReal Numbers

Teaching Mathematics through activities is a powerful approach that enhances students' understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to second student. Second student also multiplied it by a prime number and passed it to third student. In this way by multiplying to a prime number, the last student got 173250.

Now, Mukta asked some questions as given below to the students:

(i)
What is the least prime number used by students?
1 mark
(ii)
(a) How many students are in the class?
2 marks
OR
(ii)
(b) What is the highest prime number used by students?
2 marks
(iii)
Which prime number has been used maximum times?
1 mark

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Write 173250 as a product of prime factors.

Hint 2

The 2 was given by the teacher. Every other prime factor, counted with repetition, comes from one student.

Hint 3

Count how many times each prime appears in the factorisation.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Prime factorisation: $173250 = 2 \times 5^{3} \times 3^{2} \times 7 \times 11$ .
Check: $2 \times 125 \times 9 \times 77 = 173250$ .
The factor 2 is the number announced by the teacher. The remaining primes, $5, 5, 5, 3, 3, 7, 11$ , were multiplied in by the students.
(i) The primes used by the students are 3, 5, 7 and 11. The least of these is 3.
1 mark
(ii)(a) $173250 = 2 \times 5^{3} \times 3^{2} \times 7 \times 11$ . Leaving out the starting 2, the students used $5^{3} \times 3^{2} \times 7 \times 11$ .
1 mark
(ii)(a) Each student multiplied by one prime, so the number of students $= 3 + 2 + 1 + 1 = 7$ .
1 mark
(ii)(b) From $173250 = 2 \times 5^{3} \times 3^{2} \times 7 \times 11$ , the primes used by the students are 3, 5, 7 and 11.
1 mark
(ii)(b) The highest prime used is 11.
1 mark
(iii) The prime 5 appears 3 times (power $5^{3}$ ), more than any other prime. So 5 was used the maximum number of times.
1 mark

Answer: (i) 3; (ii)(a) 7 students, (ii)(b) 11; (iii) 5

Where the marks are

(i) Least prime used by the students is 3 (1 mark)
(ii)(a) Correct prime factorisation of 173250 (1 mark); counts 7 students (1 mark)
(ii)(b) Correct prime factorisation (1 mark); highest prime is 11 (1 mark)
(iii) The prime 5 is used the most times (1 mark)

Revise the chapter

Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
Topic: Fundamental Theorem of Arithmetic

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/3/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2024: question 38

Hints

Step-by-step solution

Revise the chapter

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